ABSTRACT
We begin by looking at finite difference approximations for ordinary differential equations, as they involve most of the pertinent ideas from PDE methods, yet are easier to implement. The first question we ask is the somewhat obvious question of how to approximate the first derivative. But remember the definition of f ′ using the difference quotient,
f ′(x) = lim h→0
f(x+ h)− f(x) h
.
